MinT - Best Known (168−47, 168, s)-Nets in Base 8

Best Known (168−47, 168, s)-Nets in Base 8

(168−47, 168, 1026)-Net over F₈ — Constructive and digital

Digital (121, 168, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 168, 1026)-net over F₈, using
- 4 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(168−47, 168, 5132)-Net over F₈ — Digital

Digital (121, 168, 5132)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−47, 168, 4859320)-Net in Base 8 — Upper bound on s

There is no (121, 168, 4859321)-net in base 8, because

1 times m-reduction [i] would yield (121, 167, 4859321)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 546789 875451 675763 985748 118848 538455 802996 059283 778777 743884 807201 581244 945034 626517 127588 701420 826509 756763 354412 174306 345133 562394 595997 345814 114072 > 8¹⁶⁷ [i]